Represents a layered chain in a triangulation. More...

#include <subcomplex/layeredchain.h>

Inheritance diagram for regina::LayeredChain:

Public Member Functions
	LayeredChain (Tetrahedron< 3 > *tet, Perm< 4 > vertexRoles)
	Creates a new layered chain containing only the given tetrahedron. More...

	LayeredChain (const LayeredChain &)=default
	Creates a new copy of the given structure. More...

LayeredChain &	operator= (const LayeredChain &)=default
	Sets this to be a copy of the given structure. More...

void	swap (LayeredChain &other) noexcept
	Swaps the contents of this and the given structure. More...

Tetrahedron< 3 > *	bottom () const
	Returns the bottom tetrahedron of this layered chain. More...

Tetrahedron< 3 > *	top () const
	Returns the top tetrahedron of this layered chain. More...

size_t	index () const
	Returns the number of tetrahedra in this layered chain. More...

Perm< 4 >	bottomVertexRoles () const
	Returns a permutation represeting the role that each vertex of the bottom tetrahedron plays in the layered chain. More...

Perm< 4 >	topVertexRoles () const
	Returns a permutation represeting the role that each vertex of the top tetrahedron plays in the layered chain. More...

bool	extendAbove ()
	Checks to see whether this layered chain can be extended to include the tetrahedron above the top tetrahedron (and still remain a layered chain). More...

bool	extendBelow ()
	Checks to see whether this layered chain can be extended to include the tetrahedron below the bottom tetrahedron (and still remain a layered chain). More...

bool	extendMaximal ()
	Extends this layered chain to a maximal length layered chain. More...

void	reverse ()
	Reverses this layered chain so the top tetrahedron becomes the bottom and vice versa. More...

void	invert ()
	Inverts this layered chain so the upper hinge becomes the lower and vice versa. More...

bool	operator== (const LayeredChain &other) const
	Determines whether this and the given structure represent the same type of layered chain. More...

bool	operator!= (const LayeredChain &other) const
	Determines whether this and the given structure represent different types of layered chain. More...

std::unique_ptr< Manifold >	manifold () const override
	Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...

AbelianGroup	homology () const override
	Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...

std::ostream &	writeName (std::ostream &out) const override
	Writes the name of this triangulation as a human-readable string to the given output stream. More...

std::ostream &	writeTeXName (std::ostream &out) const override
	Writes the name of this triangulation in TeX format to the given output stream. More...

void	writeTextShort (std::ostream &out) const override
	Writes a short text representation of this object to the given output stream. More...

std::string	name () const
	Returns the name of this specific triangulation as a human-readable string. More...

std::string	texName () const
	Returns the name of this specific triangulation in TeX format. More...

virtual void	writeTextLong (std::ostream &out) const
	Writes a detailed text representation of this object to the given output stream. More...

std::string	str () const
	Returns a short text representation of this object. More...

std::string	utf8 () const
	Returns a short text representation of this object using unicode characters. More...

std::string	detail () const
	Returns a detailed text representation of this object. More...

Static Public Member Functions
static std::unique_ptr< StandardTriangulation >	recognise (Component< 3 > *component)
	Determines whether the given component represents one of the standard triangulations understood by Regina. More...

static std::unique_ptr< StandardTriangulation >	recognise (const Triangulation< 3 > &tri)
	Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...

Detailed Description

Represents a layered chain in a triangulation.

A layered chain is a set of n tetrahedra glued to each other by layerings. For each tetrahedron, select two top faces, two bottom faces and two hinge edges, so that the top faces are adjacent, the bottom faces are adjacent, the hinge edges are opposite and each hinge meets both a top and a bottom face. The tetrahedron can thus be thought of as a fattened square with the top and bottom faces above and below the square respectively, and the hinges as the top and bottom edges of the square. The left and right edges of the square are identified to form an annulus.

For each i, the top faces of tetrahedron i are glued to the bottom faces of tetrahedron i+1. This is done by layering the upper tetrahedron upon the annulus formed by the top faces of the lower tetrahedron. The layering should be done over the left or right edge of the lower square (note that these two edges are actually identified). The top hinges of each tetrahedron should be identified, as should the bottom hinges.

The bottom faces of the first tetrahedron and the top faces of the last tetrahedron form the boundary of the layered chain. If there is more than one tetrahedron, the layered chain forms a solid torus with two vertices whose axis is parallel to each hinge edge.

The index of the layered chain is the number of tetrahedra it contains. A layered chain must contain at least one tetrahedron.

Note that for the purposes of manifold() and homology(), a layered chain containing only one tetrahedron will be considered as a standalone tetrahedron that forms a 3-ball (and not a solid torus).

All optional StandardTriangulation routines are implemented for this class.

This class supports copying but does not implement separate move operations, since its internal data is so small that copying is just as efficient. It implements the C++ Swappable requirement via its own member and global swap() functions, for consistency with the other StandardTriangulation subclasses.

Constructor & Destructor Documentation

◆ LayeredChain() [1/2]

regina::LayeredChain::LayeredChain	(	Tetrahedron< 3 > *	tet,
		Perm< 4 >	vertexRoles
	)

inline

Creates a new layered chain containing only the given tetrahedron.

This new layered chain will have index 1, but may be extended using extendAbove(), extendBelow() or extendMaximal().

Parameters

tet	the tetrahedron that will make up this layered chain.
vertexRoles	a permutation describing the role each tetrahedron vertex must play in the layered chain; this must be in the same format as the permutation returned by bottomVertexRoles() and topVertexRoles().

◆ LayeredChain() [2/2]

regina::LayeredChain::LayeredChain ( const LayeredChain & )

default

Creates a new copy of the given structure.

Member Function Documentation

◆ bottom()

Tetrahedron< 3 > * regina::LayeredChain::bottom ( ) const

inline

Returns the bottom tetrahedron of this layered chain.

Returns: the bottom tetrahedron.

◆ bottomVertexRoles()

Perm< 4 > regina::LayeredChain::bottomVertexRoles ( ) const

inline

Returns a permutation represeting the role that each vertex of the bottom tetrahedron plays in the layered chain.

The permutation returned (call this p) maps 0, 1, 2 and 3 to the four vertices of the bottom tetrahedron so that the edge from p[0] to p[1] is the top hinge, the edge from p[2] to p[3] is the bottom hinge, faces p[1] and p[2] are the (boundary) bottom faces and faces p[0] and p[3] are the top faces.

See the general class notes for further details.

Returns: a permutation representing the roles of the vertices of the bottom tetrahedron.

◆ detail()

std::string regina::Output< StandardTriangulation , false >::detail ( ) const

inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns: a detailed text representation of this object.

◆ extendAbove()

bool regina::LayeredChain::extendAbove ( )

Checks to see whether this layered chain can be extended to include the tetrahedron above the top tetrahedron (and still remain a layered chain).

If so, this layered chain will be modified accordingly (note that its index will be increased by one and its top tetrahedron will change).

Returns: true if and only if this layered chain was extended.

◆ extendBelow()

bool regina::LayeredChain::extendBelow ( )

Checks to see whether this layered chain can be extended to include the tetrahedron below the bottom tetrahedron (and still remain a layered chain).

If so, this layered chain will be modified accordingly (note that its index will be increased by one and its bottom tetrahedron will change).

Returns: true if and only if this layered chain was extended.

◆ extendMaximal()

bool regina::LayeredChain::extendMaximal ( )

Extends this layered chain to a maximal length layered chain.

Both extendAbove() and extendBelow() will be used until this layered chain can be extended no further.

Returns: true if and only if this layered chain was extended.

◆ homology()

AbelianGroup regina::LayeredChain::homology ( ) const

overridevirtual

Returns the expected first homology group of this triangulation, if such a routine has been implemented.

This routine does not work by calling Triangulation<3>::homology() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.

This means that homology() needs to be implemented separately for each class of standard triangulation. See the class notes for each subclass of StandardTriangulation for details on whether homology has been implemented for that particular subclass. The default implementation of this routine just throws a NotImplemented exception.

Most users will not need this routine, since presumably you already have an explicit Triangulation<3> available and so you can just call Triangulation<3>::homology() instead (which, unlike this routine, is always implemented). This StandardTriangulation::homology() routine should be seen as more of a verification/validation tool for the Regina developers.

If this StandardTriangulation describes an entire Triangulation<3> (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling Triangulation<3>::homology() upon the associated real triangulation.

Exceptions

NotImplemented	Homology calculation has not yet been implemented for this particular type of standard triangulation.
FileError	The homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusTri, which reads its results from the SnapPea census databases that are installed with Regina.

Returns: the first homology group of this triangulation, if this functionality has been implemented.

Reimplemented from regina::StandardTriangulation.

◆ index()

size_t regina::LayeredChain::index ( ) const

inline

Returns the number of tetrahedra in this layered chain.

Returns: the number of tetrahedra.

◆ invert()

void regina::LayeredChain::invert ( )

Inverts this layered chain so the upper hinge becomes the lower and vice versa.

The top and bottom tetrahedra will remain the top and bottom tetrahedra respectively.

Note that this operation will cause the hinge edges to point in the opposite direction around the solid torus formed by this layered chain.

Note that only the representation of the chain is altered; the underlying triangulation is not changed.

◆ manifold()

std::unique_ptr< Manifold > regina::LayeredChain::manifold ( ) const

overridevirtual

Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.

If the 3-manifold cannot be recognised then this routine will return null.

The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of StandardTriangulation. The default implementation of this routine returns null.

It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.

Returns: the underlying 3-manifold.

Reimplemented from regina::StandardTriangulation.

◆ name()

std::string regina::StandardTriangulation::name ( ) const

inherited

Returns the name of this specific triangulation as a human-readable string.

Returns: the name of this triangulation.

◆ operator!=()

bool regina::LayeredChain::operator!= ( const LayeredChain & other ) const

inline

Determines whether this and the given structure represent different types of layered chain.

Specifically, two layered chains will compare as equal if and only if they have the same index (i.e., the same number of tetrahedra).

This test follows the general rule for most subclasses of StandardTriangulation (excluding fixed structures such as SnappedBall and TriSolidTorus): two objects compare as equal if and only if they have the same combinatorial parameters (which for this subclass means they describe isomorphic structures).

Parameters

other the structure with which this will be compared.

Returns: true if and only if this and the given structure represent different types of layered chain.

◆ operator=()

LayeredChain & regina::LayeredChain::operator= ( const LayeredChain & )

default

Sets this to be a copy of the given structure.

Returns: a reference to this structure.

◆ operator==()

bool regina::LayeredChain::operator== ( const LayeredChain & other ) const

inline

Determines whether this and the given structure represent the same type of layered chain.

Specifically, two layered chains will compare as equal if and only if they have the same index (i.e., the same number of tetrahedra).

This test follows the general rule for most subclasses of StandardTriangulation (excluding fixed structures such as SnappedBall and TriSolidTorus): two objects compare as equal if and only if they have the same combinatorial parameters (which for this subclass means they describe isomorphic structures).

Parameters

other the structure with which this will be compared.

Returns: true if and only if this and the given structure represent the same type of layered chain.

◆ recognise() [1/2]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( Component< 3 > * component )

staticinherited

Determines whether the given component represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given component must have the same corresponding boundary triangles, i.e., the component cannot have any further identifications of these boundary triangles with each other.

Note that the triangulation-based routine recognise(const Triangulation<3>&) may recognise more triangulations than this routine, since passing an entire triangulation allows access to more information.

Parameters

component the triangulation component under examination.

Returns: the details of the standard triangulation if the given component is recognised, or null otherwise.

◆ recognise() [2/2]

static std::unique_ptr< StandardTriangulation > regina::StandardTriangulation::recognise ( const Triangulation< 3 > & tri )

staticinherited

Determines whether the given triangulation represents one of the standard triangulations understood by Regina.

The list of recognised triangulations is expected to grow between releases.

If the standard triangulation returned has boundary triangles then the given triangulation must have the same corresponding boundary triangles, i.e., the triangulation cannot have any further identifications of these boundary triangles with each other.

This routine may recognise more triangulations than the component-based recognise(Component<3>*), since passing an entire triangulation allows access to more information.

Parameters

tri	the triangulation under examination.

Returns: the details of the standard triangualation if the given triangulation is recognised, or null otherwise.

◆ reverse()

void regina::LayeredChain::reverse ( )

Reverses this layered chain so the top tetrahedron becomes the bottom and vice versa.

The upper and lower hinges will remain the upper and lower hinges respectively.

Note that this operation will cause the hinge edges to point in the opposite direction around the solid torus formed by this layered chain.

Note that only the representation of the chain is altered; the underlying triangulation is not changed.

◆ str()

std::string regina::Output< StandardTriangulation , false >::str ( ) const

inherited

Returns a short text representation of this object.

This text should be human-readable, should use plain ASCII characters where possible, and should not contain any newlines.

Within these limits, this short text ouptut should be as information-rich as possible, since in most cases this forms the basis for the Python __str__() and __repr__() functions.

Python: The Python "stringification" function __str__() will use precisely this function, and for most classes the Python __repr__() function will incorporate this into its output.

Returns: a short text representation of this object.

◆ swap()

void regina::LayeredChain::swap ( LayeredChain & other )

inlinenoexcept

Swaps the contents of this and the given structure.

Parameters

other the structure whose contents should be swapped with this.

◆ texName()

std::string regina::StandardTriangulation::texName ( ) const

inherited

Returns the name of this specific triangulation in TeX format.

No leading or trailing dollar signs will be included.

Warning: The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.

Returns: the name of this triangulation in TeX format.

◆ top()

Tetrahedron< 3 > * regina::LayeredChain::top ( ) const

inline

Returns the top tetrahedron of this layered chain.

Returns: the top tetrahedron.

◆ topVertexRoles()

Perm< 4 > regina::LayeredChain::topVertexRoles ( ) const

inline

Returns a permutation represeting the role that each vertex of the top tetrahedron plays in the layered chain.

The permutation returned (call this p) maps 0, 1, 2 and 3 to the four vertices of the top tetrahedron so that the edge from p[0] to p[1] is the top hinge, the edge from p[2] to p[3] is the bottom hinge, faces p[1] and p[2] are the bottom faces and faces p[0] and p[3] are the (boundary) top faces.

See the general class notes for further details.

Returns: a permutation representing the roles of the vertices of the top tetrahedron.

◆ utf8()

std::string regina::Output< StandardTriangulation , false >::utf8 ( ) const

inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should not contain any newlines, and (within these constraints) should be as information-rich as is reasonable.

Unlike str(), this function may use unicode characters to make the output more pleasant to read. The string that is returned will be encoded in UTF-8.

Returns: a short text representation of this object.

◆ writeName()

std::ostream & regina::LayeredChain::writeName ( std::ostream & out ) const

inlineoverridevirtual

Writes the name of this triangulation as a human-readable string to the given output stream.

Python: Not present. Instead use the variant name() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::StandardTriangulation.

◆ writeTeXName()

std::ostream & regina::LayeredChain::writeTeXName ( std::ostream & out ) const

inlineoverridevirtual

Writes the name of this triangulation in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Warning: The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.

Python: Not present. Instead use the variant texName() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::StandardTriangulation.

◆ writeTextLong()

void regina::StandardTriangulation::writeTextLong ( std::ostream & out ) const

inlinevirtualinherited

Writes a detailed text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeTextShort().

Python: Not present. Use detail() instead.

Parameters

out	the output stream to which to write.

Reimplemented in regina::AugTriSolidTorus, regina::BlockedSFS, regina::BlockedSFSLoop, regina::BlockedSFSPair, regina::BlockedSFSTriple, regina::LayeredChainPair, regina::LayeredLensSpace, regina::LayeredLoop, regina::LayeredTorusBundle, regina::PluggedTorusBundle, regina::PlugTriSolidTorus, and regina::TrivialTri.

◆ writeTextShort()

void regina::LayeredChain::writeTextShort ( std::ostream & out ) const

overridevirtual

Writes a short text representation of this object to the given output stream.

This may be reimplemented by subclasses, but the parent StandardTriangulation class offers a reasonable default implementation based on writeName().

Python: Not present. Use str() instead.

Parameters

out	the output stream to which to write.

Reimplemented from regina::StandardTriangulation.

The documentation for this class was generated from the following file:

subcomplex/layeredchain.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ LayeredChain() [1/2]

◆ LayeredChain() [2/2]

Member Function Documentation

◆ bottom()

◆ bottomVertexRoles()

◆ detail()

◆ extendAbove()

◆ extendBelow()

◆ extendMaximal()

◆ homology()

◆ index()

◆ invert()

◆ manifold()

◆ name()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ recognise() [1/2]

◆ recognise() [2/2]

◆ reverse()

◆ str()

◆ swap()

◆ texName()

◆ top()

◆ topVertexRoles()

◆ utf8()

◆ writeName()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()